Figured it out!
I was logging in with an extension, so mainly just pub key was used with signing done on a per-need basis. 
Once I logged in with private testing key, I was able to test Nip-44 DMing.

Would it make sense for Coracle's messaging to request the private key specifically for this purpose? I thought the "Decrypt messages from peers" permission that nos2x-fox asks for would be included, but seems it's not.